BASICS OF COMPUTER APPLICATIONS

ASB 102

UNIT 1Introducing computer system

Number systemWhat is number system?Types of number system Their ConversionsBinary arithmetic ( addition, subtraction,

multiplication )

Number system

• In any number system there is an ordered set of symbols known as DIGITS with rules defined for performing arithmetic operations like +, - , * etc

• A collection of these digits makes a number which in general has two parts -

1) integer

2) fractional

Set apart by a radix point (.)

• (N)b = dn-1 dn-2….di….d1 d0 . d-1 d-2…d-f….d-m

Integer portion radix fractional portion

Where

N – number

B – radix or base of the number system

n – number of digits in integer portion

m- number of digits in fractional portion

Dn-1 - most significant digit (msd )

D-m - least significant digit ( lsd )

Types of number system

• Binary number system

• Octal number system

• Decimal number system

• Hexadecimal number system

1. Binary number system

• Have base/radix 2 (two)

• Only two symbols are used to represent binary number system 0 and 1

• Eg 1011.11

2. Decimal number system

• Have base 10

• Symbols- 0,1,2,3,4,5,6,7,8,9

• Eg- 3974.57

3. Octal number system

• Have base or radix eight

• Symbols used to represent numbers- 0,1,2,3,4,5,6,7

• Eg- 3567.25

4. Hexadecimal number system

• Have base 16 which requires 16 distinct symbols to represent the numbers.

• Symbols used are 0 through 9 and alphabets A and f.

• This is an alphanumeric number system.

• Eg- 3FA9.56

Conversions - Decimal to binary

Eg1 (13)10 to ( ?)2

quotient remainder

13/ 2 6 1

6/2 3 0

3/2 1 1

½ 0 1

Thus (13)10 = ( 1101)2

• Eg ( 10.625)10 to ( ?)2

(10)10 - 1010

0.625 * 2 =1.250 1

0.250* 2 = 0.500 0

0.500* 2 = 1.000 1

101

( 10.625)10 to (1010.101)2

Conversion – binary to decimal

• eg- 110101.101

= (1*25) + (1*24) + (0*23) + (1*22) + (0*21) + (1*20) + (1*2-1) + (0*2-2) +(1*2-3)

=32 + 16 + 0 + 4 + 0 + 1

= ( 53)10